LETTERdoi:10.1038/nature12914

Rate of tree carbon accumulation increasescontinuously with tree sizeN. L. Stephenson1, A. J. Das1, R. Condit2, S. E. Russo3, P. J. Baker4, N. G. Beckman3{, D. A. Coomes5, E. R. Lines6, W. K. Morris7,N. Ruger2,8{, E. Alvarez9, C. Blundo10, S. Bunyavejchewin11, G. Chuyong12, S. J. Davies13, A. Duque14, C. N. Ewango15, O. Flores16,J. F. Franklin17, H. R. Grau10, Z. Hao18, M. E. Harmon19, S. P. Hubbell2,20, D. Kenfack13, Y. Lin21, J.-R. Makana15, A. Malizia10,L. R. Malizia22, R. J. Pabst19, N. Pongpattananurak23, S.-H. Su24, I-F. Sun25, S. Tan26, D. Thomas27, P. J. van Mantgem28, X. Wang18,S. K. Wiser29 & M. A. Zavala30

Forests are major components of the global carbon cycle, providingsubstantial feedback to atmospheric greenhouse gas concentrations1.Our ability to understand and predict changes in the forest carboncycle—particularly net primary productivity and carbon storage—increasingly relies on models that represent biological processesacross several scales of biological organization, from tree leaves toforest stands2,3. Yet, despite advances in our understanding of pro-ductivity at the scales of leaves and stands, no consensus exists aboutthe nature of productivity at the scale of the individual tree4–7, inpart because we lack a broad empirical assessment of whether ratesof absolute tree mass growth (and thus carbon accumulation) decrease,remain constant, or increase as trees increase in size and age. Here wepresent a global analysis of 403 tropical and temperate tree species,showing that for most species mass growth rate increases continu-ously with tree size. Thus, large, old trees do not act simply as se-nescent carbon reservoirs but actively fix large amounts of carboncompared to smaller trees; at the extreme, a single big tree can addthe same amount of carbon to the forest within a year as is containedin an entire mid-sized tree. The apparent paradoxes of individualtree growth increasing with tree size despite declining leaf-level8–10

and stand-level10 productivity can be explained, respectively, byincreases in a tree’s total leaf area that outpace declines in produc-tivity per unit of leaf area and, among other factors, age-relatedreductions in population density. Our results resolve conflictingassumptions about the nature of tree growth, inform efforts to under-tand and model forest carbon dynamics, and have additional impli-cations for theories of resource allocation11 and plant senescence12.

A widely held assumption is that after an initial period of increasinggrowth, the mass growth rate of individual trees declines with increas-ing tree size4,5,13–16. Although the results of a few single-species studieshave been consistent with this assumption15, the bulk of evidence citedin support of declining growth is not based on measurements of indi-vidual tree mass growth. Instead, much of the cited evidence documentseither the well-known age-related decline in net primary productivity(hereafter ‘productivity’) of even-aged forest stands10 (in which the treesare all of a similar age) or size-related declines in the rate of mass gain per

unit leaf area (or unit leaf mass)8–10, with the implicit assumption thatdeclines at these scales must also apply at the scale of the individual tree.Declining tree growth is also sometimes inferred from life-history theoryto be a necessary corollary of increasing resource allocation to reproduc-tion11,16. On the other hand, metabolic scaling theory predicts that massgrowth rate should increase continuously with tree size6, and this pre-diction has also received empirical support from a few site-specificstudies6,7. Thus, we are confronted with two conflicting generalizationsabout the fundamental nature of tree growth, but lack a global assess-ment that would allow us to distinguish clearly between them.

To fill this gap, we conducted a global analysis in which we directlyestimated mass growth rates from repeated measurements of 673,046trees belonging to 403 tropical, subtropical and temperate tree species,spanning every forested continent. Tree growth rate was modelled as afunction of log(tree mass) using piecewise regression, where the inde-pendent variable was divided into one to four bins. Conjoined linesegments were fitted across the bins (Fig. 1).

For all continents, aboveground tree mass growth rates (and, hence,rates of carbon gain) for most species increased continuously with treemass (size) (Fig. 2). The rate of mass gain increased with tree mass ineach model bin for 87% of species, and increased in the bin that includedthe largest trees for 97% of species; the majority of increases were sta-tistically significant (Table 1, Extended Data Fig. 1 and SupplementaryTable 1). Even when we restricted our analysis to species achieving thelargest sizes (maximum trunk diameter .100 cm; 33% of species), 94%had increasing mass growth rates in the bin that included the largesttrees. We found no clear taxonomic or geographic patterns among the3% of species with declining growth rates in their largest trees, althoughthe small number of these species (thirteen) hampers inference. Declin-ing species included both angiosperms and gymnosperms in seven ofthe 76 families in our study; most of the seven families had only one ortwo declining species and no family was dominated by declining spe-cies (Supplementary Table 1).

When we log-transformed mass growth rate in addition to tree mass,the resulting model fits were generally linear, as predicted by metabolicscaling theory6 (Extended Data Fig. 2). Similar to the results of our main

1US Geological Survey, Western Ecological Research Center, Three Rivers, California 93271, USA. 2Smithsonian Tropical Research Institute, Apartado 0843-03092, Balboa, Republic of Panama. 3School ofBiological Sciences, University of Nebraska, Lincoln, Nebraska 68588, USA. 4Department of Forest and Ecosystem Science, University of Melbourne, Victoria 3121, Australia. 5Department of Plant Sciences,University of Cambridge, Cambridge CB2 3EA, UK. 6Department of Geography, University College London, London WC1E 6BT, UK. 7School of Botany, University of Melbourne, Victoria 3010, Australia.8Spezielle Botanik und Funktionelle Biodiversitat, Universitat Leipzig, 04103 Leipzig, Germany. 9Jardın Botanico de Medellın, Calle 73, No. 51D-14, Medellın, Colombia. 10Instituto de Ecologıa Regional,Universidad Nacional de Tucuman, 4107 Yerba Buena, Tucuman, Argentina. 11Research Office, Department of National Parks, Wildlife and Plant Conservation, Bangkok 10900, Thailand. 12Department ofBotany and Plant Physiology, Buea, Southwest Province, Cameroon. 13Smithsonian Institution Global Earth Observatory—Center for Tropical Forest Science, Smithsonian Institution, PO Box 37012,Washington, DC 20013, USA. 14Universidad Nacional de Colombia, Departamento de Ciencias Forestales, Medellın, Colombia. 15Wildlife Conservation Society, Kinshasa/Gombe, Democratic Republic ofthe Congo. 16Unite Mixte de Recherche—Peuplements Vegetaux et Bioagresseurs en Milieu Tropical, Universite de la Reunion/CIRAD, 97410 Saint Pierre, France. 17School of Environmental and ForestSciences, University of Washington, Seattle, Washington 98195, USA. 18State Key Laboratory of Forest and Soil Ecology, Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110164,China. 19Department of Forest Ecosystems and Society, Oregon State University, Corvallis, Oregon 97331, USA. 20Department of Ecology and Evolutionary Biology, University of California, Los Angeles,California 90095, USA. 21Department of Life Science, Tunghai University, Taichung City 40704, Taiwan. 22Facultad de Ciencias Agrarias, Universidad Nacional de Jujuy, 4600 San Salvador de Jujuy,Argentina. 23Faculty of Forestry, Kasetsart University, ChatuChak Bangkok 10900, Thailand. 24Taiwan Forestry Research Institute, Taipei 10066, Taiwan. 25Department of Natural Resources andEnvironmental Studies, National Dong Hwa University, Hualien 97401, Taiwan. 26Sarawak Forestry Department, Kuching, Sarawak 93660, Malaysia. 27Department of Botany and Plant Pathology, OregonState University, Corvallis, Oregon 97331, USA. 28US Geological Survey, Western Ecological Research Center, Arcata, California 95521, USA. 29Landcare Research, PO Box 40, Lincoln 7640, New Zealand.30Forest Ecology and Restoration Group, Department of Life Sciences, University of Alcala, Alcala de Henares, 28805 Madrid, Spain. {Present addresses: Mathematical Biosciences Institute, Ohio StateUniversity, Columbus, Ohio 43210, USA (N.G.B.); German Centre for Integrative Biodiversity Research (iDiv), Halle-Jena-Leipzig, 04103 Leipzig, Germany (N.R.).

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analysis using untransformed growth, of the 381 log-transformed spe-cies analysed (see Methods), the log-transformed growth rate increasedin the bin containing the largest trees for 96% of species.

In absolute terms, trees 100 cm in trunk diameter typically add from10 kg to 200 kg of aboveground dry mass each year (depending on species),averaging 103 kg per year. This is nearly three times the rate for trees ofthe same species at 50 cm in diameter, and is the mass equivalent toadding an entirely new tree of 10–20 cm in diameter to the forest eachyear. Our findings further indicate that the extraordinary growth recentlyreported in an intensive study of large Eucalyptus regnans and Sequoiasempervirens7, which included some of the world’s most massive indi-vidual trees, is not a phenomenon limited to a few unusual species. Rather,rapid growth in giant trees is the global norm, and can exceed 600 kgper year in the largest individuals (Fig. 3).

Our data set included many natural and unmanaged forests in whichthe growth of smaller trees was probably reduced by asymmetric com-petition with larger trees. To explore the effects of competition, we cal-culated mass growth rates for 41 North American and European speciesthat had published equations for diameter growth rate in the absence ofcompetition. We found that, even in the absence of competition, 85%of the species had mass growth rates that increased continuously with treesize (Extended Data Fig. 3), with growth curves closely resembling thosein Fig. 2. Thus, our finding of increasing growth not only has broadgenerality across species, continents and forest biomes (tropical, subtropicaland temperate), it appears to hold regardless of competitive environment.

Importantly, our finding of continuously increasing growth is com-patible with the two classes of observations most often cited as evidenceof declining, rather than increasing, individual tree growth: with increas-ing tree size and age, productivity usually declines at the scales of bothtree organs (leaves) and tree populations (even-aged forest stands).

First, although growth efficiency (tree mass growth per unit leaf areaor leaf mass) often declines with increasing tree size8–10, empiricalobservations and metabolic scaling theory both indicate that, on aver-age, total tree leaf mass increases as the square of trunk diameter17,18. Atypical tree that experiences a tenfold increase in diameter will thereforeundergo a roughly 100-fold increase in total leaf mass and a 50–100-fold

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Figure 1 | Example model fits for tree mass growth rates. The species shownare the angiosperm species (Lecomtedoxa klaineana, Cameroon, 142 trees) (a)and gymnosperm species (Picea sitchensis, USA, 409 trees) (b) in our dataset that had the most massive trees (defined as those with the greatestcumulative aboveground dry mass in their five most massive trees). Each pointrepresents a single tree; the solid red lines represent best fits selected by ourmodel; and the dashed red lines indicate one standard deviation around thepredicted values.

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Figure 2 | Aboveground mass growth rates for the 403 tree species, bycontinent. a, Africa (Cameroon, Democratic Republic of the Congo); b, Asia(China, Malaysia, Taiwan, Thailand); c, Australasia (New Zealand); d, Centraland South America (Argentina, Colombia, Panama); e, Europe (Spain); and

f, North America (USA). Numbers of trees, numbers of species and percentageswith increasing growth are given in Table 1. Trunk diameters are approximatevalues for reference, based on the average diameters of trees of a given mass.

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increase in total leaf area (depending on size-related increases in leafmass per unit leaf area19,20). Parallel changes in growth efficiency canrange from a modest increase (such as in stands where small trees aresuppressed by large trees)21 to as much as a tenfold decline22, with mostchanges falling in between8,9,19,22. At one extreme, the net effect of a low(50-fold) increase in leaf area combined with a large (tenfold) decline ingrowth efficiency would still yield a fivefold increase in individual treemass growth rate; the opposite extreme would yield roughly a 100-foldincrease. Our calculated 52-fold greater average mass growth rate oftrees 100 cm in diameter compared to those 10 cm in diameter fallswithin this range. Thus, although growth efficiency often declines withincreasing tree size, increases in a tree’s total leaf area are sufficient toovercome this decline and cause whole-tree carbon accumulation rateto increase.

Second, our findings are similarly compatible with the well-knownage-related decline in productivity at the scale of even-aged forest stands.Although a review of mechanisms is beyond the scope of this paper10,23,several factors (including the interplay of changing growth efficiencyand tree dominance hierarchies24) can contribute to declining produc-tivity at the stand scale. We highlight the fact that increasing individualtree growth rate does not automatically result in increasing stand pro-ductivity because tree mortality can drive orders-of-magnitude reduc-tions in population density25,26. That is, even though the large trees inolder, even-aged stands may be growing more rapidly, such standshave fewer trees. Tree population dynamics, especially mortality, canthus be a significant contributor to declining productivity at the scale ofthe forest stand23.

For a large majority of species, our findings support metabolic scal-ing theory’s qualitative prediction of continuously increasing growth

at the scale of individual trees6, with several implications. For example,life-history theory often assumes that tradeoffs between plant growthand reproduction are substantial11. Contrary to some expectations11,16,our results indicate that for most tree species size-related changes inreproductive allocation are insufficient to drive long-term declines ingrowth rates6. Additionally, declining growth is sometimes consideredto be a defining feature of plant senescence12. Our findings are thus rele-vant to understanding the nature and prevalence of senescence in thelife history of perennial plants27.

Finally, our results are relevant to understanding and predictingforest feedbacks to the terrestrial carbon cycle and global climate system1–3.These feedbacks will be influenced by the effects of climatic, land-useand other environmental changes on the size-specific growth rates andsize structure of tree populations—effects that are already being observedin forests28,29. The rapid growth of large trees indicates that, relative totheir numbers, they could play a disproportionately important role inthese feedbacks30. For example, in our western USA old-growth forestplots, trees .100 cm in diameter comprised 6% of trees, yet contrib-uted 33% of the annual forest mass growth. Mechanistic models of theforest carbon cycle will depend on accurate representation of produc-tivity across several scales of biological organization, including calibra-tion and validation against continuously increasing carbon accumulationrates at the scale of individual trees.

METHODS SUMMARYWe estimated aboveground dry mass growth rates from consecutive diameter mea-surements of tree trunks—typically measured every five to ten years—from long-term monitoring plots. Analyses were restricted to trees with trunk diameter$10 cm, and to species having $40 trees in total and $15 trees with trunk diameter$30 cm. Maximum trunk diameters ranged from 38 cm to 270 cm among species,averaging 92 cm. We converted each diameter measurement (plus an accompany-ing height measurement for 16% of species) to aboveground dry mass, M, usingpublished allometric equations. We estimated tree growth rate as G 5DM/Dt andmodelled G as a function of log(M) for each species using piecewise regression. Theindependent variable log(M) was divided into bins and a separate line segment wasfitted to G versus log(M) in each bin so that the line segments met at the bin divi-sions. Bin divisions were not assigned a priori, but were fitted by the model sepa-rately for each species. We fitted models with 1, 2, 3 and 4 bins, and selected themodel receiving the most support by Akaike’s Information Criterion for eachspecies. Our approach thus makes no assumptions about the shape of the rela-tionship between G and log(M), and can accommodate increasing, decreasing orhump-shaped relationships. Parameters were fitted with a Gibbs sampler based onMetropolis updates, producing credible intervals for model parameters and growthrates at any diameter; uninformative priors were used for all parameters. We testedextensively for bias, and found no evidence that our results were influenced bymodel fits failing to detect a final growth decline in the largest trees, possible biasesintroduced by the 47% of species for which we combined data from several plots, orpossible biases introduced by allometric equations (Extended Data Figs 4 and 5).

Online Content Any additional Methods, Extended Data display items and SourceData are available in the online version of the paper; references unique to thesesections appear only in the online paper.

Received 5 August; accepted 27 November 2013.

Published online 15 January 2014.

1. Pan, Y. et al. A large and persistent carbon sink in the world’s forests. Science 333,988–993 (2011).

Table 1 | Sample sizes and tree growth trends by continentContinent Number of trees Number of species Percentage of species with increasing mass growth rate in the largest trees

(percentage significant at P # 0.05)

Africa 15,366 37 100.0 (86.5)Asia 43,690 136 96.3 (89.0)Australasia 45,418 22 95.5 (95.5)Central and South America 18,530 77 97.4 (92.2)Europe 439,889 42 90.5 (78.6)North America 110,153 89 98.9 (94.4)

Total 673,046 403 96.8 (89.8)

The largest trees are those in the last bin fitted by the model. Countries are listed in the legend for Fig. 2.

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Figure 3 | Aboveground mass growth rates of species in our data setcompared with E. regnans and S. sempervirens. For clarity, only the 58species in our data set having at least one tree exceeding 20 Mg are shown(lines). Data for E. regnans (green dots, 15 trees) and S. sempervirens (red dots,21 trees) are from an intensive study that included some of the most massiveindividual trees on Earth7. Both axes are expanded relative to those of Fig. 2.

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2. Medvigy, D., Wofsy, S. C., Munger, J. W., Hollinger, D. Y. & Moorcroft, P. R.Mechanistic scaling of ecosystem function and dynamics in space and time:Ecosystem Demography model version 2. J. Geophys. Res. 114, G01002 (2009).

3. Caspersen, J. P., Vanderwel, M. C., Cole, W. G. & Purves, D. W. How standproductivity results from size- and competition-dependent growth and mortality.PLoS ONE 6, e28660 (2011).

4. Kutsch, W. L. et al. in Old-Growth Forests: Function, Fate and Value (eds Wirth, C.,Gleixner, G. & Heimann, M.) 57–79 (Springer, 2009).

5. Meinzer, F. C., Lachenbruch,B.& Dawson, T. E. (eds) Size- and Age-RelatedChangesin Tree Structure and Function (Springer, 2011).

6. Enquist, B. J., West, G. B., Charnov, E. L. & Brown, J. H. Allometric scaling ofproduction and life-history variation in vascular plants. Nature 401, 907–911(1999).

7. Sillett, S. C. et al. Increasing wood production through old age in tall trees. For. Ecol.Manage. 259, 976–994 (2010).

8. Mencuccini, M. et al. Size-mediated ageing reduces vigour in trees. Ecol. Lett. 8,1183–1190 (2005).

9. Drake, J. E., Raetz, L. M., Davis, S. C. & DeLucia, E. H. Hydraulic limitation notdeclining nitrogen availability causes the age-related photosynthetic decline inloblolly pine (Pinus taeda L.). Plant Cell Environ. 33, 1756–1766 (2010).

10. Ryan, M. G., Binkley, D. & Fownes, J. H. Age-related decline in forest productivity:pattern and process. Adv. Ecol. Res. 27, 213–262 (1997).

11. Thomas, S. C. in Size- and Age-Related Changes in Tree Structure and Function(eds Meinzer, F. C., Lachenbruch, B. & Dawson, T. E.) 33–64 (Springer, 2011).

12. Thomas, H. Senescence, ageing and death of the whole plant. New Phytol. 197,696–711 (2013).

13. Carey, E. V., Sala, A., Keane, R. & Callaway, R. M. Are old forests underestimated asglobal carbon sinks? Glob. Change Biol. 7, 339–344 (2001).

14. Phillips, N. G., Buckley, T. N. & Tissue, D. T. Capacity of old trees to respond toenvironmental change. J. Integr. Plant Biol. 50, 1355–1364 (2008).

15. Piper, F. I. & Fajardo, A. No evidence of carbon limitation with tree age andheight inNothofagus pumilio under Mediterranean and temperate climate conditions. Ann.Bot. 108, 907–917 (2011).

16. Weiner, J.& Thomas, S.C. Thenature of treegrowth and the ‘‘age-relateddecline inforest productivity’’. Oikos 94, 374–376 (2001).

17. Jenkins, J. C., Chojnacky, D. C., Heath, L. S. & Birdsey, R. A. Comprehensive Databaseof Diameter-based Biomass Regressions for North American Tree Species GeneralTechnical Report NE-319, http://www.nrs.fs.fed.us/pubs/6725 (USDA ForestService, Northeastern Research Station, 2004).

18. Niklas, K. J. & Enquist, B. J. Canonical rules for plant organ biomass partitioningand annual allocation. Am. J. Bot. 89, 812–819 (2002).

19. Thomas, S. C. Photosynthetic capacity peaks at intermediate size in temperatedeciduous trees. Tree Physiol. 30, 555–573 (2010).

20. Steppe, K., Niinemets, U. & Teskey, R. O. in Size- and Age-Related Changes in TreeStructure and Function (eds Meinzer, F. C., Lachenbruch, B. & Dawson, T. E.)235–253 (Springer, 2011).

21. Gilmore, D. W. & Seymour, R. S. Alternative measures of stem growth efficiencyapplied to Abies balsamea from four canopy positions in central Maine, USA. For.Ecol. Manage. 84, 209–218 (1996).

22. Kaufmann, M. R. & Ryan, M. G. Physiographic, stand, and environmental effects onindividual tree growth and growth efficiency in subalpine forests. Tree Physiol. 2,47–59 (1986).

23. Coomes, D. A., Holdaway, R. J., Kobe, R. K., Lines, E. R. & Allen, R. B. A generalintegrative framework for modelling woody biomass production and carbonsequestration rates in forests. J. Ecol. 100, 42–64 (2012).

24. Binkley, D. A hypothesis about the interaction of tree dominance and standproduction through stand development. For. Ecol. Manage. 190, 265–271 (2004).

25. Pretzsch, H. & Biber, P. A re-evaluation of Reineke’s rule and stand density index.For. Sci. 51, 304–320 (2005).

26. Kashian, D. M., Turner, M. G., Romme, W. H. & Lorimer, C. G. Variability andconvergence in stand structural development on a fire-dominated subalpinelandscape. Ecology 86, 643–654 (2005).

27. Munne-Bosch, S. Do perennials really senesce? Trends Plant Sci. 13, 216–220(2008).

28. Jump, A. S., Hunt, J. M. & Penuelas, J. Rapid climate change-related growth declineat the southern range edge of Fagus sylvatica. Glob. Change Biol. 12, 2163–2174(2006).

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Supplementary Information is available in the online version of the paper.

Acknowledgements We thank the hundreds of people who have established andmaintained the forest plots and their associated databases; M. G. Ryan for commentson the manuscript; C. D. Canham and T. Hart for supplying data; C. D. Canham fordiscussions and feedback; J. S. Baron for hosting our workshops; and Spain’sMinisterio de Agricultura, Alimentacion y Medio Ambiente (MAGRAMA) for grantingaccess to the Spanish Forest Inventory Data. Our analyses were supported by theUnited States Geological Survey (USGS) John Wesley Powell Center for Analysis andSynthesis, the USGS Ecosystems and Climate and Land Use Change mission areas, theSmithsonian Institution Global Earth Observatory—Center for Tropical Forest Science(CTFS), and a University of Nebraska-Lincoln Program of Excellence in PopulationBiology Postdoctoral Fellowship (to N.G.B.). In addition, X.W.was supported byNationalNatural Science Foundation of China (31370444) and State Key Laboratory of Forestand Soil Ecology (LFSE2013-11). Data collection was funded by a broad range oforganizations including the USGS, the CTFS, the US National Science Foundation, theAndrews LTER (NSF-LTER DEB-0823380), the US National Park Service, the US ForestService (USFS), the USFS Forest Inventory and Analysis Program, the John D. andCatherine T. MacArthur Foundation, the Andrew W. Mellon Foundation, MAGRAMA, theCouncil of Agriculture of Taiwan, the National Science Council of Taiwan, the NationalNatural Science Foundation of China, the Knowledge Innovation Program of theChinese Academy of Sciences, Landcare Research and the National Vegetation SurveyDatabase (NVS) of New Zealand, the French Fund for the Global Environment andFundacion ProYungas. This paper is a contribution from the Western MountainInitiative, a USGS global change research project. Any use of trade names is fordescriptive purposes only and does not imply endorsement by the USA government.

Author Contributions N.L.S. and A.J.D. conceived the study with feedback from R.C.and D.A.C., N.L.S., A.J.D., R.C. and S.E.R. wrote the manuscript. R.C. devised the mainanalytical approach and wrote the computer code. N.L.S., A.J.D., R.C., S.E.R., P.J.B.,N.G.B., D.A.C., E.R.L., W.K.M. and N.R. performed analyses. N.L.S., A.J.D., R.C., S.E.R.,P.J.B., D.A.C., E.R.L., W.K.M., E.A., C.B., S.B., G.C., S.J.D., A.D., C.N.E., O.F., J.F.F., H.R.G., Z.H.,M.E.H., S.P.H., D.K., Y.L., J.-R.M., A.M., L.R.M., R.J.P., N.P., S.-H.S., I-F.S., S.T., D.T., P.J.v.M.,X.W., S.K.W. and M.A.Z. supplied data and sources of allometric equations appropriateto their data.

Author Information Fitted model parameters for each species have been deposited inUSGS’s ScienceBase at http://dx.doi.org/10.5066/F7JS9NFM. Reprints andpermissions information is available at www.nature.com/reprints. The authors declareno competing financial interests. Readers are welcome to comment on the onlineversion of the paper. Correspondence and requests for materials should be addressedto N.L.S. (nstephenson@usgs.gov).

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METHODSData. We required that forest monitoring plots provided unbiased samples of allliving trees within the plot boundaries, and that the trees had undergone two trunkdiameter measurements separated by at least one year. Some plots sampled min-imally disturbed old (all-aged) forest, whereas others, particularly those associatedwith national inventories, sampled forest stands regardless of past managementhistory. Plots are described in the references cited in Supplementary Table 1.

Our raw data were consecutive measurements of trunk diameter, D, with mostmeasurements taken 5 to 10 years apart (range, 1–29 years). D was measured at astandard height on the trunk (usually 1.3–1.4 m above ground level), consistentacross measurements for a tree. Allometric equations for 16% of species required, inaddition to consecutive measurements of D, consecutive measurements of tree height.

We excluded trees exhibiting extreme diameter growth, defined as trunks whereD increased by $40 mm yr21 or that shrank by $12s, where s is the standarddeviation of the D measurement error, s 5 0.9036 1 0.006214D (refs 31, 32); out-liers of these magnitudes were almost certainly due to error. By being so liberal inallowing negative growth anomalies, we erred on the side of reducing our abilityto detect increases in tree mass growth rate. Using other exclusion values yieldedsimilar results, as did a second approach to handling error in which we reanalyseda subset of our models using a Bayesian method that estimates growth rates afteraccounting for error, based on independent plot-specific data quantifying mea-surement error33.

To standardize minimum D among data sets, we analysed only trees with D $ 10 cmat the first census. To ensure adequate samples of trees spanning a broad range ofsizes, we restricted analyses to species having both $40 trees in total and also $15trees with D $ 30 cm at the first census. This left us with 673,046 trees belonging to403 tropical and temperate species in 76 families, spanning twelve countries and allforested continents (Supplementary Table 1). Maximum trunk diameters rangedfrom 38 cm to 270 cm among species, and averaged 92 cm.Estimating tree mass. To estimate each tree’s aboveground dry mass, M, we usedpublished allometric equations relating M to D (or for 16% of species, relating M toD and tree height). Some equations were species-specific and others were specificto higher taxonomic levels or forest types, described in the references in Supplemen-tary Table 1. The single tropical moist forest equation of ref. 34 was applied to mosttropical species, whereas most temperate species had unique species-specific equa-tions. Most allometric equations are broadly similar, relating log(M) to log(D)linearly, or nearly linearly—a familiar relationship in allometric scaling of bothanimals and plants35. Equations can show a variety of differences in detail, how-ever, with some adding log(D) squared and cubed terms. All equations make use ofthe wood density of individual species, but when wood density was not available fora given species we used mean wood density for a genus or family36.

Using a single, average allometry for most tropical species, and mean wood den-sity for a genus or family for several species, limits the accuracy of our estimates ofM. However, because we treat each species separately, it makes no difference whetherour absolute M estimates are more accurate in some species than in others, onlythat they are consistent within a species and therefore accurately reveal whethermass growth rates increase or decrease with tree size.

For two regions—Spain and the western USA—allometric equations estimatedmass only for a tree’s main stem rather than all aboveground parts, includingbranches and leaves. But because leaf and stem masses are positively correlatedand their growth rates are expected to scale isometrically both within and amongspecies18,37,38, results from these two regions should not alter our qualitative con-clusions. Confirming this, the percentage of species with increasing stem massgrowth rate in the last bin for Spain and the western USA (93.4% of 61 species) wassimilar to that from the remainder of regions (97.4% of 342 species) (P 5 0.12,Fisher’s exact test).Modelling mass growth rate. We sought a modelling approach that made noassumptions about the shape of the relationship between aboveground dry massgrowth rate, G, and aboveground dry mass, M, and that could accommodatemonotonically increasing, monotonically decreasing, or hump-shaped relation-ships. We therefore chose to model G as a function of log(M) using piecewise linearregression. The range of the x axis, X 5 log(M), is divided into a series of bins, andwithin each bin G is fitted as a function of X by linear regression. The position ofthe bins is adaptive: it is fitted along with the regression terms. Regression lines arerequired to meet at the boundary between bins. For a single model-fitting run thenumber of bins, B, is fixed. For example, if B 5 2, there are four parameters to befitted for a single species: the location of the boundary between bins, X1; the slopeof the regression in the first bin, S1; the slope in the second bin, S2; and an interceptterm. Those four parameters completely define the model. In general, there are 2Bparameters for B bins.

Growth rates, while approximately normally distributed, were heteroskedastic,with the variance increasing with mass (Fig. 1), so an additional model was neededfor the standard deviation of G, sG, as a function of log(M). The increase of sG

with log(M) was clearly not linear, so we used a three-parameter model:

sG~k for log Mð Þvdð Þ

sG~azblog Mð Þ (for log Mð Þ§d)

where the intercept a is determined by the values of k, d and b. Thus sG wasconstant for smaller values of log(M) (below the cutoff d), then increased linearlyfor larger log(M) (Fig. 1). The parameters k, d and b were estimated along with theparameters of the growth model.

Parameters of both the growth and standard deviation models were estimated ina Bayesian framework using the likelihood of observing growth rates given modelpredictions and the estimated standard deviation of the Gaussian error function. AMarkov chain Monte Carlo chain of parameter estimates was created using a Gibbssampler with a Metropolis update39,40 written in the programming language R(ref. 41) (a tutorial and the computer code are available through http://ctfs.arnarb.harvard.edu/Public/CTFSRPackage/files/tutorials/growthfitAnalysis). The samplerworks by updating each of the parameters in sequence, holding other parametersfixed while the relevant likelihood function is used to locate the target parameter’snext value. The step size used in the updates was adjusted adaptively through theruns, allowing more rapid convergence40. The final Markov chain Monte Carlochain describes the posterior distribution for each model parameter, the error, andwas then used to estimate the posterior distribution of growth rates as estimatedfrom the model. Priors on model parameters were uniform over an unlimitedrange, whereas the parameters describing the standard deviation were restrictedto .0. Bin boundaries, Xi, were constrained as follows: (1) boundaries could onlyfall within the range of X, (2) each bin contained at least five trees, and (3) no binspanned less than 10% of the range of X. The last two restrictions prevented thebins from collapsing to very narrow ranges of X in which the fitted slope might takeabsurd extremes.

We chose piecewise regression over other alternatives for modelling G as afunction of M for two main reasons. First, the linear regression slopes within eachbin provide precise statistical tests of whether G increases or decreases with X,based on credible intervals of the slope parameters. Second, with adaptive binpositions, the function is completely flexible in allowing changes in slope at anypoint in the X range, with no influence of any one bin on the others. In contrast, inparametric models where a single function defines the relationship across all X, theshape of the curve at low X can (and indeed must) influence the shape at high X,hindering statistical inference about changes in tree growth at large size.

We used log(M) as our predictor because within a species M has a highly non-Gaussian distribution, with many small trees and only a few very large trees, includ-ing some large outliers. In contrast, we did not log-transform our dependent variableG so that we could retain values of G # 0 that are often recorded in very slowlygrowing trees, for which diameter change over a short measurement interval can beon a par with diameter measurement error.

For each species, models with 1, 2, 3 and 4 bins were fitted. Of these four models,the model receiving the greatest weight of evidence by Akaike Information Criterion(AIC) was selected. AIC is defined as the log-likelihood of the best-fitting model,penalized by twice the number of parameters. Given that adding one more bin to amodel meant two more parameters, the model with an extra bin had to improve thelog-likelihood by 4 to be considered a better model42.Assessing model fits. To determine whether our approach might have failed toreveal a final growth decline within the few largest trees of the various species, wecalculated mass growth rate residuals for the single most massive individual treeof each species. For 52% of the 403 species, growth of the most massive tree wasunderestimated by our model fits (for example, Fig. 1a); for 48% it was overestimated(for example, Fig. 1b). These proportions were indistinguishable from 50% (P 5 0.55,binomial test), as would be expected for unbiased model fits. Furthermore, themean residual (observed minus predicted) mass growth rate of these most massivetrees, 10.006 Mg yr21, was statistically indistinguishable from zero (P 5 0.29, two-tailed t-test). We conclude that our model fits accurately represent growth trendsup through, and including, the most massive trees.Effects of combined data. To achieve sample sizes adequate for analysis, for somespecies we combined data from several different forest plots, potentially intro-ducing a source of bias: if the largest trees of a species disproportionately occur onproductive sites, the increase in mass growth rate with tree size could be exagger-ated. This might occur because trees on less-productive sites—presumably the siteshaving the slowest-growing trees within any given size class—could be under-represented in the largest size classes. We assessed this possibility in two ways.

First, our conclusions remained unchanged when we compared results for the53% of species that came uniquely from single large plots with those of the 47% ofspecies whose data were combined across several plots. Proportions of species withincreasing mass growth rates in the last bin were indistinguishable between the twogroups (97.6% and 95.8%, respectively; P 5 0.40, Fisher’s exact test). Additionally,

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the shapes and magnitudes of the growth curves for Africa and Asia, where datafor each species came uniquely from single large plots, were similar to those ofAustralasia, Europe and North America, where data for each species were combinedacross several plots (Table 1, Fig. 2 and Extended Data Fig. 2). (Data from Centraland South America were from both single and combined plots, depending onspecies.)

Second, for a subset of combined-data species we compared two sets of modelfits: (1) using all available plots (that is, the analyses we present in the main text),and (2) using only plots that contained massive trees—those in the top 5% of massfor a species. To maximize our ability to detect differences, we limited these analysesto species with large numbers of trees found in a large number of plots, dispersedwidely across a broad geographic region. We therefore analysed the twelve Spanishspecies that each had more than 10,000 individual trees (Supplementary Table 1),found in 34,580 plots distributed across Spain. Massive trees occurred in 6,588(19%) of the 34,580 plots. We found no substantial differences between the twoanalyses. When all 34,580 plots were analysed, ten of the twelve species showedincreasing growth in the last bin, and seven showed increasing growth across allbins; when only the 6,588 plots containing the most massive trees were analysed,the corresponding numbers were eleven and nine. Model fits for the two groupswere nearly indistinguishable in shape and magnitude across the range of tree masses.We thus found no evidence that the potential for growth differences among plotsinfluenced our conclusions.Effects of possible allometric biases. For some species, the maximum trunk dia-meter D in our data sets exceeded the maximum used to calibrate the species’ allo-metric equation. In such cases our estimates of M extrapolate beyond the fittedallometry and could therefore be subject to bias. For 336 of our 403 species we wereable to determine D of the largest tree that had been used in calibrating the associatedallometric equations. Of those 336 species, 74% (dominated by tropical species)had no trees in our data set with D exceeding that used in calibrating the allometricequations, with the remaining 26% (dominated by temperate species) having atleast one tree with D exceeding that used in calibration. The percentage of specieswith increasing G in the last bin for the first group (98.0%) was indistinguishablefrom that of the second group (96.6%) (P 5 0.44, Fisher’s exact test). Thus, ourfinding of increasing G with tree size is not affected by the minority of species thathave at least one tree exceeding the maximum value of D used to calibrate theirassociated allometric equations.

A bias that could inflate the rate at which G increases with tree size could arise ifallometric equations systematically underestimate M for small trees or overestimateM for large trees43. For a subset of our study species we obtained the raw data—consisting of measured values of D and M for individual trees—needed to calibrateallometric equations, allowing us to determine whether the particular form of thosespecies’ allometric equations was prone to bias, and if so, the potential consequencesof that bias.

To assess the potential for allometric bias for the majority (58%) of speciesin our data set—those that used the empirical moist tropical forest equation ofref. 34—we reanalysed the data provided by ref. 34. The data were from 1,504harvested trees representing 60 families and 184 genera, with D ranging from 5 cmto 156 cm; the associated allometric equation relates log(M) to a third-order poly-nomial of log(D). Because the regression of M on D was fitted on a log–log scale,this and subsequent equations include a correction of exp[(RSE)2/2] for the errorin back-transformation, where RSE is the residual standard error from the statist-ical model44. Residuals of M for the equation revealed no evident biases (ExtendedData Fig. 4a), suggesting that we should expect little (if any) systematic size-relatedbiases in our estimates of G for the 58% of our species that used this equation.

Our simplest form of allometric equation—applied to 22% of our species—waslog(M) 5 a 1 blog(D), where a and b are taxon-specific constants. For nine of ourspecies that used equations of this form (all from the temperate western USA:Abies amabilis, A. concolor, A. procera, Pinus lambertiana, Pinus ponderosa, Piceasitchensis, Pseudotsuga menziesii, Tsuga heterophylla and T. mertensiana) we hadvalues of both D and M for a total of 1,358 individual trees, allowing us to fitspecies-specific allometric equations of the form log(M) 5 a 1 blog(D) and thenassess them for bias. Residual plots showed a tendency to overestimate M for thelargest trees (Extended Data Fig. 4b), with the possible consequence of inflatingestimates of G for the largest relative to the smallest trees of these species.

To determine whether this bias was likely to alter our qualitative conclusion thatG increases with tree size, we created a new set of allometric relations between Dand M —one for each of the nine species—using the same piecewise linear regres-sion approach we used to model G as a function of M. However, because our goalwas to eliminate bias rather than seek the most parsimonious model, we fixed thenumber of bins at four, with the locations of boundaries between the bins beingfitted by the model. Our new allometry using piecewise regressions led to predic-tions of M with no apparent bias relative to D (Extended Data Fig. 4c). This new,unbiased allometry gave the same qualitative results as our original, simple allometry

regarding the relationship between G and M: for all nine species, G increased in thebin containing the largest trees, regardless of the allometry used (Extended DataFig. 5). We conclude that any bias associated with the minority of our species thatused the simple allometric equation form was unlikely to affect our broad conclu-sion that G increases with tree size in a majority of tree species.

As a final assessment, we compared our results to those of a recent study ofE. regnans and S. sempervirens, in which M and G had been calculated from inten-sive measurements of aboveground portions of trees without the use of standardallometric equations7. Specifically, in two consecutive years 36 trees of differentsizes and ages were climbed, trunk diameters were systematically measured at severalheights, branch diameters and lengths were measured (with subsets of foliage andbranches destructively sampled to determine mass relationships), wood densitieswere determined and ring widths from increment cores were used to supplementmeasured diameter growth increments. The authors used these measurements tocalculate M for each of the trees in each of the two consecutive years, and G as thedifference in M between the two years7. E. regnans and S. sempervirens are theworld’s tallest angiosperm and gymnosperm species, respectively, so the data setwas dominated by exceptionally large trees; most had M $ 20 Mg, and M of someindividuals exceeded that of the most massive trees in our own data set (whichlacked E. regnans and S. sempervirens). We therefore compared E. regnans andS. sempervirens to the 58 species in our data set that had at least one individualwith M $ 20 Mg. Sample sizes for E. regnans and S. sempervirens—15 and 21 trees,respectively—fell below our required $40 trees for fitting piecewise linear regres-sions, so we simply plotted data points for individual E. regnans and S. sempervirensalong with the piecewise regressions that we had already fitted for our 58 compar-ison species (Fig. 3).

As reported by ref. 7, G increased with M for both E. regnans and S. sempervirens,up to and including some of the most massive individual trees on the Earth (Fig. 3).Within the zone of overlapping M between the two data sets, G values for indi-vidual E. regnans and S. sempervirens trees fell almost entirely within the ranges ofthe piecewise regressions we had fitted for our 58 comparison species. We takethese observations as a further indication that our results, produced using standardallometric equations, accurately reflect broad relationships between M and G.Fitting log–log models. To model log(G) as a function of log(M), we used thebinning approach that we used in our primary analysis of mass growth rate (describedearlier). However, in log-transforming growth we dropped trees with G # 0. Becausenegative growth rates become more extreme with increasing tree size, droppingthem could introduce a bias towards increasing growth rates. Log-transformationadditionally resulted in skewed growth rate residuals. Dropping trees with G # 0caused several species to fall below our threshold sample size, reducing the totalnumber of species analysed to 381 (Extended Data Fig. 2).Growth in the absence of competition. We obtained published equations for 41North American and European species, in 46 species-site combinations, relatingspecies-specific tree diameter growth rates to trunk diameter D and to neighbour-hood competition45–49. Setting neighbourhood competition to zero gave us equa-tions describing estimated annual D growth as a function of D in the absence ofcompetition. Starting at D0 5 10 cm, we sequentially (1) calculated annual D growthfor a tree of size Dt, (2) added this amount to Dt to determine Dt 1 1, (3) used anappropriate taxon-specific allometric equation to calculate the associated treemasses Mt and Mt11, and (iv) calculated tree mass growth rate Gt of a tree of massMt in the absence of competition as Mt 1 1 2 Mt. For each of the five species thathad separate growth analyses available from two different sites, we required thatmass growth rate increased continuously with tree size at both sites for the speciesto be considered to have a continuously increasing mass growth rate. North Americanand European allometries were taken from refs 17 and 50, respectively, with pre-ference given to allometric equations based on power functions of tree diameter,large numbers of sampled trees, and trees spanning a broad range of diameters. Forthe 47% of European species for which ref. 50 had no equations meeting ourcriteria, we used the best-matched (by species or genus) equations from ref. 17.

31. Condit, R. et al. Tropical forest dynamics across a rainfall gradient and the impactof an El Nino dry season. J. Trop. Ecol. 20, 51–72 (2004).

32. Condit, R. et al. The importance of demographic niches to tree diversity. Science313, 98–101 (2006).

33. Ruger, N., Berger, U., Hubbell, S. P., Vieilledent, G. & Condit, R. Growth strategies oftropical tree species: disentangling light and size effects. PLoS ONE 6, e25330(2011).

34. Chave, J. et al. Tree allometry and improved estimation of carbon stocks andbalance in tropical forests. Oecologia 145, 87–99 (2005).

35. Sibly, R. M., Brown, J. H. & Kodric-Brown, A. (eds) Metabolic Ecology: A ScalingApproach (John Wiley & Sons, 2012).

36. Zanne, A. E. et al. Data from: Towards a worldwide wood economics spectrum.In Dryad Digital Data Repository, http://dx.doi.org/10.5061/dryad.234 (2009).

37. Enquist, B. J. & Niklas, K. J. Global allocation rules for patterns of biomasspartitioning in seed plants. Science 295, 1517–1520 (2002).

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38. Niklas, K. J. Plant allometry: is there a grand unifying theory? Biol. Rev. 79,871–889 (2004).

39. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E.Equation of state calculations by fast computing machines. J. Chem. Phys. 21,1087–1092 (1953).

40. Ruger, N., Huth, A., Hubbell, S. P. & Condit, R. Determinants of mortality across atropical lowland rainforest community. Oikos 120, 1047–1056 (2011).

41. R Development Core Team. R: A Language and Environment for StatisticalComputing (R Foundation for Statistical Computing, 2009).

42. Hilborn, R. & Mangel, M. The Ecological Detective: Confronting Models with Data(Princeton Univ. Press, 1997).

43. Chambers, J. Q., Dos Santos, J., Ribeiro, R. J. & Higuchi, N. Tree damage, allometricrelationships, and above-ground net primary production in central Amazon forest.For. Ecol. Manage. 152, 73–84 (2001).

44. Baskerville, G. L. Use of logarithmic regression in the estimation of plant biomass.Can. J. For. Res. 2, 49–53 (1972).

45. Canham, C. D. et al. Neighborhood analyses of canopy tree competition alongenvironmental gradients in New England forests. Ecol. Appl. 16, 540–554 (2006).

46. Coates, K. D., Canham, C. D. & LePage, P. T. Above- versus below-groundcompetitive effects and responses of a guild of temperate tree species. J. Ecol. 97,118–130 (2009).

47. Pretzsch, H. & Biber, P. Size-symmetric versus size-asymmetric competition andgrowth partitioning among trees in forest stands along an ecological gradient incentral Europe. Can. J. For. Res. 40, 370–384 (2010).

48. Gomez-Aparicio, L., Garcıa-Valdes, R., Ruız-Benito, P. & Zavala, M. A. Disentanglingthe relative importance of climate, size and competition on tree growth in Iberianforests: implications for forest management under global change. Glob. ChangeBiol. 17, 2400–2414 (2011).

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Extended Data Figure 1 | Summary of model fits for tree mass growth rates.Bars show the percentage of species with mass growth rates that increase withtree mass for each bin; black shading indicates percentage significant atP # 0.05. Tree masses increase with bin number. a, Species fitted with one bin(165 species); b, Species fitted with two bins (139 species); c, Species fitted withthree bins (56 species); and d, Species fitted with four bins (43 species).

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Extended Data Figure 2 | Log–log model fits of mass growth rates for 381tree species, by continent. Trees with growth rates # 0 were dropped from theanalysis, reducing the number of species meeting our threshold sample sizefor analysis. a, Africa (33 species); b, Asia (123 species); c, Australasia

(22 species); d, Central and South America (73 species); e, Europe (41 species);and f, North America (89 species). Trunk diameters are approximate values forreference, based on the average diameters of trees of a given mass.

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Extended Data Figure 3 | Aboveground mass growth rates for 41 treespecies in the absence of competition. The ‘1’ or ‘2’ symbol preceding eachspecies code indicates, respectively, species with mass growth rates thatincreased continuously with tree size or species with mass growth rates thatdeclined in the largest trees. Sources of the diameter growth equations used tocalculate mass growth were: a, ref. 45; b, ref. 46; c, ref. 48; d, ref. 47; and e, ref. 49.ABAM, Abies amabilis; ABBA, Abies balsamea; ABCO, Abies concolor; ABLA,Abies lasiocarpa; ABMA, Abies magnifica; ACRU, Acer rubrum; ACSA, Acersaccharum; BEAL, Betula alleghaniensis; BELE, Betula lenta; BEPA, Betulapapyrifera; CADE, Calocedrus decurrens; CASA, Castanea sativa; FAGR, Fagusgrandifolia; FASY, Fagus sylvatica; FRAM, Fraxinus americana; JUTH,

Juniperus thurifera; PIAB, Picea abies; PICO, Pinus contorta; PIHA, Pinushalepensis; PIHY, Picea hybrid (a complex of Picea glauca, P. sitchensis andP. engelmannii); PILA, Pinus lambertiana; PINI, Pinus nigra; PIPINA, Pinuspinaster; PIPINE, Pinus pinea; PIRU, Picea rubens; PIST, Pinus strobus; PISY,Pinus sylvestris; PIUN, Pinus uncinata; POBA, Populus balsamifera ssp.trichocarpa; POTR, Populus tremuloides; PRSE, Prunus serotina; QUFA,Quercus faginea; QUIL, Quercus ilex; QUPE, Quercus petraea; QUPY, Quercuspyrenaica; QURO, Quercus robar; QURU, Quercus rubra; QUSU, Quercussuber; THPL, Thuja plicata; TSCA, Tsuga canadensis; and TSHE, Tsugaheterophylla.

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Extended Data Figure 4 | Residuals of predicted minus observed tree mass.a, The allometric equation for moist tropical forests34—used for the majority oftree species—shows no evident systematic bias in predicted aboveground drymass, M, relative to trunk diameter (n 5 1,504 trees). b, In contrast, oursimplest form of allometric equation—used for 22% of our species and hereapplied to nine temperate species—shows an apparent bias towardsoverestimating M for large trees (n 5 1,358 trees). c, New allometries thatwe created for the nine temperate species removed the apparent bias inpredicted M.

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Extended Data Figure 5 | Estimated mass growth rates of the ninetemperate species of Extended Data Fig. 4. Growth was estimated using thesimplest form of allometric model [log(M) 5 a 1 blog(D)] (a) and ourallometric models fitted with piecewise linear regression (b). Regardless of theallometric model form, all nine species show increasing G in the largest trees.

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